pacman::p_load(maptools, sf, raster, spatstat, tmap)In-Class Exercise 4: Spatial Point Patterns Analysis
Alt: Hands-On Exercise 4 & 5 - Spatial Point Patterns Analysis
Import Relevant Packages
Spatial Data Wrangling
# Import childcare spatial data
childcare_sf <- st_read("data/child-care-services-geojson.geojson") %>%
st_transform(crs = 3414)Reading layer `child-care-services-geojson' from data source
`/Users/michelle/Desktop/IS415/shelle-mim/IS415-GAA/Hands-on_Exercise/Wk4/data/child-care-services-geojson.geojson'
using driver `GeoJSON'
Simple feature collection with 1545 features and 2 fields
Geometry type: POINT
Dimension: XYZ
Bounding box: xmin: 103.6824 ymin: 1.248403 xmax: 103.9897 ymax: 1.462134
z_range: zmin: 0 zmax: 0
Geodetic CRS: WGS 84# Import coastal spatial data
sg_sf <- st_read(dsn = "data", layer="CostalOutline")Reading layer `CostalOutline' from data source
`/Users/michelle/Desktop/IS415/shelle-mim/IS415-GAA/Hands-on_Exercise/Wk4/data'
using driver `ESRI Shapefile'
Simple feature collection with 60 features and 4 fields
Geometry type: POLYGON
Dimension: XY
Bounding box: xmin: 2663.926 ymin: 16357.98 xmax: 56047.79 ymax: 50244.03
Projected CRS: SVY21# Import ura spatial data
mpsz_sf <- st_read(dsn = "data",
layer = "MP14_SUBZONE_WEB_PL")Reading layer `MP14_SUBZONE_WEB_PL' from data source
`/Users/michelle/Desktop/IS415/shelle-mim/IS415-GAA/Hands-on_Exercise/Wk4/data'
using driver `ESRI Shapefile'
Simple feature collection with 323 features and 15 fields
Geometry type: MULTIPOLYGON
Dimension: XY
Bounding box: xmin: 2667.538 ymin: 15748.72 xmax: 56396.44 ymax: 50256.33
Projected CRS: SVY21Assign correct CRS
sg_sf <- st_transform(sg_sf, 3414)
st_geometry(sg_sf)Geometry set for 60 features
Geometry type: POLYGON
Dimension: XY
Bounding box: xmin: 2663.926 ymin: 16357.98 xmax: 56047.79 ymax: 50244.03
Projected CRS: SVY21 / Singapore TM
First 5 geometries:mpsz_sf <- st_transform(mpsz_sf, 3414)
st_geometry(mpsz_sf)Geometry set for 323 features
Geometry type: MULTIPOLYGON
Dimension: XY
Bounding box: xmin: 2667.538 ymin: 15748.72 xmax: 56396.44 ymax: 50256.33
Projected CRS: SVY21 / Singapore TM
First 5 geometries:st_geometry(childcare_sf)Geometry set for 1545 features
Geometry type: POINT
Dimension: XYZ
Bounding box: xmin: 11203.01 ymin: 25667.6 xmax: 45404.24 ymax: 49300.88
z_range: zmin: 0 zmax: 0
Projected CRS: SVY21 / Singapore TM
First 5 geometries:All data is now in SVY21.
Mapping
# Static map of chilcares
tmap_mode("plot")
tm_shape(mpsz_sf) +
tm_polygons() +
tm_shape(childcare_sf) +
tm_dots(size = 0.002)
# Interactive Map
tmap_mode('view')
tm_shape(childcare_sf)+
tm_dots()tmap_mode('plot')Geospatial Data Wrangling
# Convert sf data to sp spatial class
childcare <- as_Spatial(childcare_sf)
mpsz <- as_Spatial(mpsz_sf)
sg <- as_Spatial(sg_sf)# Display info
list(childcare)[[1]]
class : SpatialPointsDataFrame
features : 1545
extent : 11203.01, 45404.24, 25667.6, 49300.88 (xmin, xmax, ymin, ymax)
crs : +proj=tmerc +lat_0=1.36666666666667 +lon_0=103.833333333333 +k=1 +x_0=28001.642 +y_0=38744.572 +ellps=WGS84 +towgs84=0,0,0,0,0,0,0 +units=m +no_defs
variables : 2
names : Name, Description
min values : kml_1, <center><table><tr><th colspan='2' align='center'><em>Attributes</em></th></tr><tr bgcolor="#E3E3F3"> <th>ADDRESSBLOCKHOUSENUMBER</th> <td></td> </tr><tr bgcolor=""> <th>ADDRESSBUILDINGNAME</th> <td></td> </tr><tr bgcolor="#E3E3F3"> <th>ADDRESSPOSTALCODE</th> <td>018989</td> </tr><tr bgcolor=""> <th>ADDRESSSTREETNAME</th> <td>1, MARINA BOULEVARD, #B1 - 01, ONE MARINA BOULEVARD, SINGAPORE 018989</td> </tr><tr bgcolor="#E3E3F3"> <th>ADDRESSTYPE</th> <td></td> </tr><tr bgcolor=""> <th>DESCRIPTION</th> <td></td> </tr><tr bgcolor="#E3E3F3"> <th>HYPERLINK</th> <td></td> </tr><tr bgcolor=""> <th>LANDXADDRESSPOINT</th> <td>0</td> </tr><tr bgcolor="#E3E3F3"> <th>LANDYADDRESSPOINT</th> <td>0</td> </tr><tr bgcolor=""> <th>NAME</th> <td>THE LITTLE SKOOL-HOUSE INTERNATIONAL PTE. LTD.</td> </tr><tr bgcolor="#E3E3F3"> <th>PHOTOURL</th> <td></td> </tr><tr bgcolor=""> <th>ADDRESSFLOORNUMBER</th> <td></td> </tr><tr bgcolor="#E3E3F3"> <th>INC_CRC</th> <td>08F73931F4A691F4</td> </tr><tr bgcolor=""> <th>FMEL_UPD_D</th> <td>20200826094036</td> </tr><tr bgcolor="#E3E3F3"> <th>ADDRESSUNITNUMBER</th> <td></td> </tr></table></center>
max values : kml_999, <center><table><tr><th colspan='2' align='center'><em>Attributes</em></th></tr><tr bgcolor="#E3E3F3"> <th>ADDRESSBLOCKHOUSENUMBER</th> <td></td> </tr><tr bgcolor=""> <th>ADDRESSBUILDINGNAME</th> <td></td> </tr><tr bgcolor="#E3E3F3"> <th>ADDRESSPOSTALCODE</th> <td>829646</td> </tr><tr bgcolor=""> <th>ADDRESSSTREETNAME</th> <td>200, PONGGOL SEVENTEENTH AVENUE, SINGAPORE 829646</td> </tr><tr bgcolor="#E3E3F3"> <th>ADDRESSTYPE</th> <td></td> </tr><tr bgcolor=""> <th>DESCRIPTION</th> <td>Child Care Services</td> </tr><tr bgcolor="#E3E3F3"> <th>HYPERLINK</th> <td></td> </tr><tr bgcolor=""> <th>LANDXADDRESSPOINT</th> <td>0</td> </tr><tr bgcolor="#E3E3F3"> <th>LANDYADDRESSPOINT</th> <td>0</td> </tr><tr bgcolor=""> <th>NAME</th> <td>RAFFLES KIDZ @ PUNGGOL PTE LTD</td> </tr><tr bgcolor="#E3E3F3"> <th>PHOTOURL</th> <td></td> </tr><tr bgcolor=""> <th>ADDRESSFLOORNUMBER</th> <td></td> </tr><tr bgcolor="#E3E3F3"> <th>INC_CRC</th> <td>379D017BF244B0FA</td> </tr><tr bgcolor=""> <th>FMEL_UPD_D</th> <td>20200826094036</td> </tr><tr bgcolor="#E3E3F3"> <th>ADDRESSUNITNUMBER</th> <td></td> </tr></table></center> list(mpsz)[[1]]
class : SpatialPolygonsDataFrame
features : 323
extent : 2667.538, 56396.44, 15748.72, 50256.33 (xmin, xmax, ymin, ymax)
crs : +proj=tmerc +lat_0=1.36666666666667 +lon_0=103.833333333333 +k=1 +x_0=28001.642 +y_0=38744.572 +ellps=WGS84 +towgs84=0,0,0,0,0,0,0 +units=m +no_defs
variables : 15
names : OBJECTID, SUBZONE_NO, SUBZONE_N, SUBZONE_C, CA_IND, PLN_AREA_N, PLN_AREA_C, REGION_N, REGION_C, INC_CRC, FMEL_UPD_D, X_ADDR, Y_ADDR, SHAPE_Leng, SHAPE_Area
min values : 1, 1, ADMIRALTY, AMSZ01, N, ANG MO KIO, AM, CENTRAL REGION, CR, 00F5E30B5C9B7AD8, 16409, 5092.8949, 19579.069, 871.554887798, 39437.9352703
max values : 323, 17, YUNNAN, YSSZ09, Y, YISHUN, YS, WEST REGION, WR, FFCCF172717C2EAF, 16409, 50424.7923, 49552.7904, 68083.9364708, 69748298.792 list(sg)[[1]]
class : SpatialPolygonsDataFrame
features : 60
extent : 2663.926, 56047.79, 16357.98, 50244.03 (xmin, xmax, ymin, ymax)
crs : +proj=tmerc +lat_0=1.36666666666667 +lon_0=103.833333333333 +k=1 +x_0=28001.642 +y_0=38744.572 +ellps=WGS84 +towgs84=0,0,0,0,0,0,0 +units=m +no_defs
variables : 4
names : GDO_GID, MSLINK, MAPID, COSTAL_NAM
min values : 1, 1, 0, ISLAND LINK
max values : 60, 67, 0, SINGAPORE - MAIN ISLAND # Convert to generic sp object
childcare_sp <- as(childcare, "SpatialPoints")
sg_sp <- as(sg, "SpatialPolygons")childcare_spclass : SpatialPoints
features : 1545
extent : 11203.01, 45404.24, 25667.6, 49300.88 (xmin, xmax, ymin, ymax)
crs : +proj=tmerc +lat_0=1.36666666666667 +lon_0=103.833333333333 +k=1 +x_0=28001.642 +y_0=38744.572 +ellps=WGS84 +towgs84=0,0,0,0,0,0,0 +units=m +no_defs sg_spclass : SpatialPolygons
features : 60
extent : 2663.926, 56047.79, 16357.98, 50244.03 (xmin, xmax, ymin, ymax)
crs : +proj=tmerc +lat_0=1.36666666666667 +lon_0=103.833333333333 +k=1 +x_0=28001.642 +y_0=38744.572 +ellps=WGS84 +towgs84=0,0,0,0,0,0,0 +units=m +no_defs # convert to spatstat's ppp format
childcare_ppp <- as(childcare_sp, "ppp")
childcare_pppPlanar point pattern: 1545 points
window: rectangle = [11203.01, 45404.24] x [25667.6, 49300.88] unitsplot(childcare_ppp)
# statistics
summary(childcare_ppp)Planar point pattern: 1545 points
Average intensity 1.91145e-06 points per square unit
*Pattern contains duplicated points*
Coordinates are given to 3 decimal places
i.e. rounded to the nearest multiple of 0.001 units
Window: rectangle = [11203.01, 45404.24] x [25667.6, 49300.88] units
(34200 x 23630 units)
Window area = 808287000 square units# check for duplicated points (warning also appears in summary)
any(duplicated(childcare_ppp))[1] TRUE# find number of duiplicated points
# multiplicity() shows all points
sum(multiplicity(childcare_ppp) > 1)[1] 128# observe duplicated points (higher opacity spots on the map)
tmap_mode('view')
tm_shape(childcare) +
tm_dots(alpha=0.4,
size=0.05)tmap_mode('plot')Methods of Removing duplicate points
#1: Delete duplicated points => but removes useful data
#2: Jittering: add small perturbation so duplicate points are not in same place
childcare_ppp_jit <- rjitter(childcare_ppp,
retry=TRUE,
nsim=1,
drop=TRUE)any(duplicated(childcare_ppp_jit))[1] FALSE#3: Make each point unique, then attached duplicates as marks (attributes of the points) => needs analytical techniques to take into account marks
Creating owin object
Used to create a geographical area to confine analysis within
sg_owin <- as(sg_sp, "owin")plot(sg_owin)
summary(sg_owin)Window: polygonal boundary
60 separate polygons (no holes)
vertices area relative.area
polygon 1 38 1.56140e+04 2.09e-05
polygon 2 735 4.69093e+06 6.27e-03
polygon 3 49 1.66986e+04 2.23e-05
polygon 4 76 3.12332e+05 4.17e-04
polygon 5 5141 6.36179e+08 8.50e-01
polygon 6 42 5.58317e+04 7.46e-05
polygon 7 67 1.31354e+06 1.75e-03
polygon 8 15 4.46420e+03 5.96e-06
polygon 9 14 5.46674e+03 7.30e-06
polygon 10 37 5.26194e+03 7.03e-06
polygon 11 53 3.44003e+04 4.59e-05
polygon 12 74 5.82234e+04 7.78e-05
polygon 13 69 5.63134e+04 7.52e-05
polygon 14 143 1.45139e+05 1.94e-04
polygon 15 165 3.38736e+05 4.52e-04
polygon 16 130 9.40465e+04 1.26e-04
polygon 17 19 1.80977e+03 2.42e-06
polygon 18 16 2.01046e+03 2.69e-06
polygon 19 93 4.30642e+05 5.75e-04
polygon 20 90 4.15092e+05 5.54e-04
polygon 21 721 1.92795e+06 2.57e-03
polygon 22 330 1.11896e+06 1.49e-03
polygon 23 115 9.28394e+05 1.24e-03
polygon 24 37 1.01705e+04 1.36e-05
polygon 25 25 1.66227e+04 2.22e-05
polygon 26 10 2.14507e+03 2.86e-06
polygon 27 190 2.02489e+05 2.70e-04
polygon 28 175 9.25904e+05 1.24e-03
polygon 29 1993 9.99217e+06 1.33e-02
polygon 30 38 2.42492e+04 3.24e-05
polygon 31 24 6.35239e+03 8.48e-06
polygon 32 53 6.35791e+05 8.49e-04
polygon 33 41 1.60161e+04 2.14e-05
polygon 34 22 2.54368e+03 3.40e-06
polygon 35 30 1.08382e+04 1.45e-05
polygon 36 327 2.16921e+06 2.90e-03
polygon 37 111 6.62927e+05 8.85e-04
polygon 38 90 1.15991e+05 1.55e-04
polygon 39 98 6.26829e+04 8.37e-05
polygon 40 415 3.25384e+06 4.35e-03
polygon 41 222 1.51142e+06 2.02e-03
polygon 42 107 6.33039e+05 8.45e-04
polygon 43 7 2.48299e+03 3.32e-06
polygon 44 17 3.28303e+04 4.38e-05
polygon 45 26 8.34758e+03 1.11e-05
polygon 46 177 4.67446e+05 6.24e-04
polygon 47 16 3.19460e+03 4.27e-06
polygon 48 15 4.87296e+03 6.51e-06
polygon 49 66 1.61841e+04 2.16e-05
polygon 50 149 5.63430e+06 7.53e-03
polygon 51 609 2.62570e+07 3.51e-02
polygon 52 8 7.82256e+03 1.04e-05
polygon 53 976 2.33447e+07 3.12e-02
polygon 54 55 8.25379e+04 1.10e-04
polygon 55 976 2.33447e+07 3.12e-02
polygon 56 61 3.33449e+05 4.45e-04
polygon 57 6 1.68410e+04 2.25e-05
polygon 58 4 9.45963e+03 1.26e-05
polygon 59 46 6.99702e+05 9.35e-04
polygon 60 13 7.00873e+04 9.36e-05
enclosing rectangle: [2663.93, 56047.79] x [16357.98, 50244.03] units
(53380 x 33890 units)
Window area = 748741000 square units
Fraction of frame area: 0.414# Combining point events with owin
childcareSG_ppp = childcare_ppp[sg_owin]
summary(childcareSG_ppp)Planar point pattern: 1545 points
Average intensity 2.063463e-06 points per square unit
*Pattern contains duplicated points*
Coordinates are given to 3 decimal places
i.e. rounded to the nearest multiple of 0.001 units
Window: polygonal boundary
60 separate polygons (no holes)
vertices area relative.area
polygon 1 38 1.56140e+04 2.09e-05
polygon 2 735 4.69093e+06 6.27e-03
polygon 3 49 1.66986e+04 2.23e-05
polygon 4 76 3.12332e+05 4.17e-04
polygon 5 5141 6.36179e+08 8.50e-01
polygon 6 42 5.58317e+04 7.46e-05
polygon 7 67 1.31354e+06 1.75e-03
polygon 8 15 4.46420e+03 5.96e-06
polygon 9 14 5.46674e+03 7.30e-06
polygon 10 37 5.26194e+03 7.03e-06
polygon 11 53 3.44003e+04 4.59e-05
polygon 12 74 5.82234e+04 7.78e-05
polygon 13 69 5.63134e+04 7.52e-05
polygon 14 143 1.45139e+05 1.94e-04
polygon 15 165 3.38736e+05 4.52e-04
polygon 16 130 9.40465e+04 1.26e-04
polygon 17 19 1.80977e+03 2.42e-06
polygon 18 16 2.01046e+03 2.69e-06
polygon 19 93 4.30642e+05 5.75e-04
polygon 20 90 4.15092e+05 5.54e-04
polygon 21 721 1.92795e+06 2.57e-03
polygon 22 330 1.11896e+06 1.49e-03
polygon 23 115 9.28394e+05 1.24e-03
polygon 24 37 1.01705e+04 1.36e-05
polygon 25 25 1.66227e+04 2.22e-05
polygon 26 10 2.14507e+03 2.86e-06
polygon 27 190 2.02489e+05 2.70e-04
polygon 28 175 9.25904e+05 1.24e-03
polygon 29 1993 9.99217e+06 1.33e-02
polygon 30 38 2.42492e+04 3.24e-05
polygon 31 24 6.35239e+03 8.48e-06
polygon 32 53 6.35791e+05 8.49e-04
polygon 33 41 1.60161e+04 2.14e-05
polygon 34 22 2.54368e+03 3.40e-06
polygon 35 30 1.08382e+04 1.45e-05
polygon 36 327 2.16921e+06 2.90e-03
polygon 37 111 6.62927e+05 8.85e-04
polygon 38 90 1.15991e+05 1.55e-04
polygon 39 98 6.26829e+04 8.37e-05
polygon 40 415 3.25384e+06 4.35e-03
polygon 41 222 1.51142e+06 2.02e-03
polygon 42 107 6.33039e+05 8.45e-04
polygon 43 7 2.48299e+03 3.32e-06
polygon 44 17 3.28303e+04 4.38e-05
polygon 45 26 8.34758e+03 1.11e-05
polygon 46 177 4.67446e+05 6.24e-04
polygon 47 16 3.19460e+03 4.27e-06
polygon 48 15 4.87296e+03 6.51e-06
polygon 49 66 1.61841e+04 2.16e-05
polygon 50 149 5.63430e+06 7.53e-03
polygon 51 609 2.62570e+07 3.51e-02
polygon 52 8 7.82256e+03 1.04e-05
polygon 53 976 2.33447e+07 3.12e-02
polygon 54 55 8.25379e+04 1.10e-04
polygon 55 976 2.33447e+07 3.12e-02
polygon 56 61 3.33449e+05 4.45e-04
polygon 57 6 1.68410e+04 2.25e-05
polygon 58 4 9.45963e+03 1.26e-05
polygon 59 46 6.99702e+05 9.35e-04
polygon 60 13 7.00873e+04 9.36e-05
enclosing rectangle: [2663.93, 56047.79] x [16357.98, 50244.03] units
(53380 x 33890 units)
Window area = 748741000 square units
Fraction of frame area: 0.414plot(childcareSG_ppp)
First-Order Spatial Point Pattern Analysis
Kernel Density Estimation
# bw.diggle = automatic bandwith selection. can also use bw.CvL(), bw.scott(), bw.ppl()
# kernel = smooting kernel/selected smoothing method (others: epanechnikov, quartic, disc)
kde_childcareSG_bw <- density(childcareSG_ppp,
sigma=bw.diggle,
edge=TRUE,
kernel="gaussian") plot(kde_childcareSG_bw)
# Retrieve the bandwith used to computer kde layer
bw <- bw.diggle(childcareSG_ppp)
bw sigma
298.4095 # Rescaling KDE values (convert unit of measurement)
childcareSG_ppp.km <- rescale(childcareSG_ppp, 1000, "km")kde_childcareSG.bw <- density(childcareSG_ppp.km, sigma=bw.diggle, edge=TRUE, kernel="gaussian")
plot(kde_childcareSG.bw)
Other bandwidth calc methods:
bw.CvL(childcareSG_ppp.km) sigma
4.543278 bw.scott(childcareSG_ppp.km) sigma.x sigma.y
2.224898 1.450966 bw.ppl(childcareSG_ppp.km) sigma
0.3897114 bw.diggle(childcareSG_ppp.km) sigma
0.2984095 # Compare outputs of bw.diggle vs bw.ppl
kde_childcareSG.ppl <- density(childcareSG_ppp.km,
sigma=bw.ppl,
edge=TRUE,
kernel="gaussian")
par(mfrow=c(1,2))
plot(kde_childcareSG.bw, main = "bw.diggle")
plot(kde_childcareSG.ppl, main = "bw.ppl")
# Different kernel methods
par(mfrow=c(2,2))
plot(density(childcareSG_ppp.km,
sigma=bw.ppl,
edge=TRUE,
kernel="gaussian"),
main="Gaussian")
plot(density(childcareSG_ppp.km,
sigma=bw.ppl,
edge=TRUE,
kernel="epanechnikov"),
main="Epanechnikov")
plot(density(childcareSG_ppp.km,
sigma=bw.ppl,
edge=TRUE,
kernel="quartic"),
main="Quartic")
plot(density(childcareSG_ppp.km,
sigma=bw.ppl,
edge=TRUE,
kernel="disc"),
main="Disc")
Fixed & Adaptive KDE
# Compute KDE with bw of 600m (sigma=0.6)
kde_childcareSG_600 <- density(childcareSG_ppp.km, sigma=0.6, edge=TRUE, kernel="gaussian")
plot(kde_childcareSG_600)
# KDE with adaptive bandwith
kde_childcareSG_adaptive <- adaptive.density(childcareSG_ppp.km, method="kernel")
plot(kde_childcareSG_adaptive)
# Compared fixed vs adaptive
par(mfrow=c(1,2))
plot(kde_childcareSG.bw, main = "Fixed bandwidth")
plot(kde_childcareSG_adaptive, main = "Adaptive bandwidth")
# KDE output into grid
gridded_kde_childcareSG_bw <- as.SpatialGridDataFrame.im(kde_childcareSG.bw)
spplot(gridded_kde_childcareSG_bw)
# grid to raster
kde_childcareSG_bw_raster <- raster(gridded_kde_childcareSG_bw)kde_childcareSG_bw_rasterclass : RasterLayer
dimensions : 128, 128, 16384 (nrow, ncol, ncell)
resolution : 0.4170614, 0.2647348 (x, y)
extent : 2.663926, 56.04779, 16.35798, 50.24403 (xmin, xmax, ymin, ymax)
crs : NA
source : memory
names : v
values : -1.005814e-14, 28.51831 (min, max)# include crs info into raster
projection(kde_childcareSG_bw_raster) <- CRS("+init=EPSG:3414")
kde_childcareSG_bw_rasterclass : RasterLayer
dimensions : 128, 128, 16384 (nrow, ncol, ncell)
resolution : 0.4170614, 0.2647348 (x, y)
extent : 2.663926, 56.04779, 16.35798, 50.24403 (xmin, xmax, ymin, ymax)
crs : +init=EPSG:3414
source : memory
names : v
values : -1.005814e-14, 28.51831 (min, max)# visualise output
tm_shape(kde_childcareSG_bw_raster) +
tm_raster("v") +
tm_layout(legend.position = c("right", "bottom"), frame = FALSE)
Comparing spatial point patterns using KDE
# Extract areas for analysis
pg = mpsz[mpsz@data$PLN_AREA_N == "PUNGGOL",]
tm = mpsz[mpsz@data$PLN_AREA_N == "TAMPINES",]
ck = mpsz[mpsz@data$PLN_AREA_N == "CHOA CHU KANG",]
jw = mpsz[mpsz@data$PLN_AREA_N == "JURONG WEST",]# plot
par(mfrow=c(2,2))
plot(pg, main = "Ponggol")
plot(tm, main = "Tampines")
plot(ck, main = "Choa Chu Kang")
plot(jw, main = "Jurong West")
# convert to sp
pg_sp = as(pg, "SpatialPolygons")
tm_sp = as(tm, "SpatialPolygons")
ck_sp = as(ck, "SpatialPolygons")
jw_sp = as(jw, "SpatialPolygons")# convert to owin
pg_owin = as(pg_sp, "owin")
tm_owin = as(tm_sp, "owin")
ck_owin = as(ck_sp, "owin")
jw_owin = as(jw_sp, "owin")# extract childcare in regions
childcare_pg_ppp = childcare_ppp_jit[pg_owin]
childcare_tm_ppp = childcare_ppp_jit[tm_owin]
childcare_ck_ppp = childcare_ppp_jit[ck_owin]
childcare_jw_ppp = childcare_ppp_jit[jw_owin]# rescale to transform unit of measurement
childcare_pg_ppp.km = rescale(childcare_pg_ppp, 1000, "km")
childcare_tm_ppp.km = rescale(childcare_tm_ppp, 1000, "km")
childcare_ck_ppp.km = rescale(childcare_ck_ppp, 1000, "km")
childcare_jw_ppp.km = rescale(childcare_jw_ppp, 1000, "km")# Plot
par(mfrow=c(2,2))
plot(childcare_pg_ppp.km, main="Punggol")
plot(childcare_tm_ppp.km, main="Tampines")
plot(childcare_ck_ppp.km, main="Choa Chu Kang")
plot(childcare_jw_ppp.km, main="Jurong West")
# computer KDE
par(mfrow=c(2,2))
plot(density(childcare_pg_ppp.km,
sigma=bw.diggle,
edge=TRUE,
kernel="gaussian"),
main="Punggol")
plot(density(childcare_tm_ppp.km,
sigma=bw.diggle,
edge=TRUE,
kernel="gaussian"),
main="Tempines")
plot(density(childcare_ck_ppp.km,
sigma=bw.diggle,
edge=TRUE,
kernel="gaussian"),
main="Choa Chu Kang")
plot(density(childcare_jw_ppp.km,
sigma=bw.diggle,
edge=TRUE,
kernel="gaussian"),
main="JUrong West")
# compute fixed bandwith KDE
par(mfrow=c(2,2))
plot(density(childcare_ck_ppp.km,
sigma=0.25,
edge=TRUE,
kernel="gaussian"),
main="Chou Chu Kang")
plot(density(childcare_jw_ppp.km,
sigma=0.25,
edge=TRUE,
kernel="gaussian"),
main="JUrong West")
plot(density(childcare_pg_ppp.km,
sigma=0.25,
edge=TRUE,
kernel="gaussian"),
main="Punggol")
plot(density(childcare_tm_ppp.km,
sigma=0.25,
edge=TRUE,
kernel="gaussian"),
main="Tampines")
Nearest Neighbour Analysis
# Clark-Evans test of aggregation
clarkevans.test(childcareSG_ppp,
correction="none",
clipregion="sg_owin",
alternative=c("clustered"),
nsim=99)
Clark-Evans test
No edge correction
Monte Carlo test based on 99 simulations of CSR with fixed n
data: childcareSG_ppp
R = 0.54756, p-value = 0.01
alternative hypothesis: clustered (R < 1)# C-E test for CCK
clarkevans.test(childcare_ck_ppp,
correction="none",
clipregion=NULL,
alternative=c("two.sided"),
nsim=999)
Clark-Evans test
No edge correction
Monte Carlo test based on 999 simulations of CSR with fixed n
data: childcare_ck_ppp
R = 0.96077, p-value = 0.166
alternative hypothesis: two-sided# C-E test for Tamp
clarkevans.test(childcare_tm_ppp,
correction="none",
clipregion=NULL,
alternative=c("two.sided"),
nsim=999)
Clark-Evans test
No edge correction
Monte Carlo test based on 999 simulations of CSR with fixed n
data: childcare_tm_ppp
R = 0.81478, p-value = 0.002
alternative hypothesis: two-sidedSecond-Order Spatial Point Pattern Analysis
G Function
# Compute G-function using Gest()
G_CK = Gest(childcare_ck_ppp, correction = "border")
plot(G_CK, xlim=c(0,500))
# Monte Carlo test with G-function
G_CK.csr <- envelope(childcare_ck_ppp, Gest, nsim = 999)Generating 999 simulations of CSR ...
1, 2, 3, ......10.........20.........30.........40.........50.........60........
.70.........80.........90.........100.........110.........120.........130......
...140.........150.........160.........170.........180.........190.........200....
.....210.........220.........230.........240.........250.........260.........270..
.......280.........290.........300.........310.........320.........330.........340
.........350.........360.........370.........380.........390.........400........
.410.........420.........430.........440.........450.........460.........470......
...480.........490.........500.........510.........520.........530.........540....
.....550.........560.........570.........580.........590.........600.........610..
.......620.........630.........640.........650.........660.........670.........680
.........690.........700.........710.........720.........730.........740........
.750.........760.........770.........780.........790.........800.........810......
...820.........830.........840.........850.........860.........870.........880....
.....890.........900.........910.........920.........930.........940.........950..
.......960.........970.........980.........990........ 999.
Done.plot(G_CK.csr)
# Compute G-func for Tamp
G_tm = Gest(childcare_tm_ppp, correction = "best")
plot(G_tm)
# Monte-Carole Test: Hypo test for random distribution in Tamp (H0=rand, H1=not rand)
G_tm.csr <- envelope(childcare_tm_ppp, Gest, correction = "all", nsim = 999)Generating 999 simulations of CSR ...
1, 2, 3, ......10.........20.........30.........40.........50.........60........
.70.........80.........90.........100.........110.........120.........130......
...140.........150.........160.........170.........180.........190.........200....
.....210.........220.........230.........240.........250.........260.........270..
.......280.........290.........300.........310.........320.........330.........340
.........350.........360.........370.........380.........390.........400........
.410.........420.........430.........440.........450.........460.........470......
...480.........490.........500.........510.........520.........530.........540....
.....550.........560.........570.........580.........590.........600.........610..
.......620.........630.........640.........650.........660.........670.........680
.........690.........700.........710.........720.........730.........740........
.750.........760.........770.........780.........790.........800.........810......
...820.........830.........840.........850.........860.........870.........880....
.....890.........900.........910.........920.........930.........940.........950..
.......960.........970.........980.........990........ 999.
Done.plot(G_tm.csr)
F Function
# Compute F-func on CCK
F_CK = Fest(childcare_ck_ppp)
plot(F_CK)
# Monte-Carole Test: Hypo testing for randomness (H0=rand, H1=not rand)
F_CK.csr <- envelope(childcare_ck_ppp, Fest, nsim = 999)Generating 999 simulations of CSR ...
1, 2, 3, ......10.........20.........30.........40.........50.........60........
.70.........80.........90.........100.........110.........120.........130......
...140.........150.........160.........170.........180.........190.........200....
.....210.........220.........230.........240.........250.........260.........270..
.......280.........290.........300.........310.........320.........330.........340
.........350.........360.........370.........380.........390.........400........
.410.........420.........430.........440.........450.........460.........470......
...480.........490.........500.........510.........520.........530.........540....
.....550.........560.........570.........580.........590.........600.........610..
.......620.........630.........640.........650.........660.........670.........680
.........690.........700.........710.........720.........730.........740........
.750.........760.........770.........780.........790.........800.........810......
...820.........830.........840.........850.........860.........870.........880....
.....890.........900.........910.........920.........930.........940.........950..
.......960.........970.........980.........990........ 999.
Done.# Plot results => lies within envelope, so can conclude is random (H0)
plot(F_CK.csr)